Gromov's Compactness Theorem for Pseudo-Holomorphic Curves

By Christoph Hummel

Mikhail Gromov introduced pseudo-holomorphic curves into symplectic geometry in 1985. Since then, pseudo-holomorphic curves have taken on great importance in many fields. The aim of this book is to present the original proof of Gromov's compactness theorem for pseudo-holomorphic curves in detail. Local properties of pseudo-holomorphic curves are investigated and proved from a geometric viewpoint. Properties of particular interest are isoperimetric inequalities, a monotonicity formula, gradient bounds and the removal of singularities. A special chapter is devoted to relevant features of hyperbolic surfaces, where pairs of pants decomposition and thickthin decomposition are described. The book is essentially self-contained and should also be accessible to students with a basic knowledge of differentiable manifolds and covering spaces.

• Format: Hardcover
• Language: English
• ISBN: 3764357355
• ISBN13: 9783764357351
• Release Date: May 1997
• Publisher: Birkhauser
• Length: 135 Pages
• Weight: 0.90 lbs.
• Dimensions: 0.4" x 6.1" x 9.2"